INVOLUTION, in arithmetic is the operation of raising a number to any power, rolling it up, as it were, by continued multi plication. Before the invention of a satisfactory symbol like or the Greeks spoke of the second power as a "tetragon number" (Terplrycovos aptOpOs, tetrag' onos arithmos', four-angled number) or a "power" (Svvapts, dy'namis, whence also "dynamo" and "dy namite"). Diophantus (c. 275) called the third power a cube (id/0os, cu'bos, see CUBE), the fourth power a "power-power" (ovv aktobbv a/2(s dynamody'namis), a fifth power a "power-cube" and so on, using the additive principle.
Involution is the converse of evolution (q.v.), which is the operation of finding a root. See ARITHMETIC. In geometry, an involution is a one-to-one correspondence between two ranges of points or between two pencils. See PROJECTIVE GEOMETRY. The "involute" of a curve is the locus of the end of a string when unwrapped from the curve itself.
Zeus to give her the heifer, set Argus Panoptes to watch her. Zeus thereupon sent Hermes, who lulled Argus to sleep and cut off his head or killed him with a stone. But the wrath of Hera still pursued Io. Maddened by a gadfly sent by the goddess, she wandered all over the earth (Aesch. P.V., 561, et seq.), swam the strait known on this account as the Bosporus (Ox-ford), and crossed the Ionian sea (traditionally called after her) until at last she reached Egypt, where she was restored to her original form and became the mother of Epaphus. She was thus identified with Isis, and Epaphus with Apis. • He was said to have been carried off by order of Hera to Byblus in Syria, where he was found again by Io. This fable connects Io with the Syrian Astarte. Both legends reflect intercourse with the East and identification of foreign with Greek gods. She was a favourite subject among Greek painters, and many representations are preserved on vases and wall paintings.